Project Grant 2208392

This National Science Foundation project grant of $199,968 supports collaborative research at Tufts University from September 2022 through August 2025 under the Mathematical and Physical Sciences program (CFDA 47.049). The research aims to advance theory and computation for structured sensing problems involving low-rank matrix recovery from deterministically structured measurements. Specifically, the project will study scalable non-convex optimization methods for generalized matrix completion problems with measurement structures informed by applications like robust structure prediction and machine learning. Researchers will design algorithms leveraging tools from high-dimensional probability, Riemannian optimization, numerical analysis, and spectral graph theory. The work focuses on analyzing local convergence of a Riemannian gradient descent approach, developing an algorithm for the Euclidean distance geometry problem, and designing fast, robust methods for cases where measurements may be sparsely corrupted. Findings are expected to contribute to recovery guarantees for these problems. The award also supports training students in distance geometry, optimization theory, and computational science.